I. INTRODUCTION
Distributed energy storage systems (DESS) play an important role in microgrids [1]. With DESS, a microgrid can realize a seamless switching between the grid-connected and stand-alone operation modes. This can provide uninterrupted power supplying for critical loads in the microgrid when a grid power outage or fault occurs. Secondly, DESS can import the excessive power generated by renewable distributed generation (DG) units in a microgrid, and export the power when the DG units cannot meet the demanding power of the loads. In this way, the fluctuation of the power flow between the main grid and the microgrid is suppressed during grid-connected operation, and it is possible to realize an uninterrupted power supply for an autonomous microgrid [2].
One-power-stage line-interactive UPS systems [3]-[5], whose typical topology is shown in Fig. 1, are good candidates for providing energy storage within a microgrid. They can exchange power with DG units and deliver power to the load efficiently. More importantly, they can directly parallel with the main grid and the microgrid, which allows them to form a true and low-cost distributed energy storage system within a microgrid.
Fig. 1.Typical topology of the line-interactive UPS.
In order to achieve a reliable and flexible microgrid, the line-interactive UPS is required to switch seamlessly between the grid-connected mode and the stand-alone parallel mode [5], [6]. In order to achieve this objective, many control strategies have been reported. One category of control strategies is based on hybrid voltage and current control. The inverter operates in the current-controlled mode to regulate the current injected into the point of common coupling (PCC) in the grid-tied mode, while in the stand-alone mode, the inverter switches to the voltage-controlled mode to regulate the output voltage across the load [7]-[11]. The advantage of this category of strategies is that the power control has a good dynamic performance due to the wide bandwidth of the current loop in the grid-connected mode. However, if the power demand of the UPS is not matched with the load power the moment the grid fails, the voltage across the load may be driven out of the normal range before the voltage loop functions. To mitigate this voltage transient, a novel voltage loop was proposed in [12], which is connected in series with the current loop. However, it saturates in grid-tied operation, and can be automatically activated to regulate the load voltage upon the occurrence of islanding.
Another category of control strategies to achieve smooth mode transitions is based on the UPS being controlled to be a voltage source all the time during mode transitions while the additional outer controllers are used to control the power flow [13], [14]. The advantage of this type of methods is that the load voltage can be uninterruptedly controlled within a permitted range by the UPS during mode transitions. In [14], one outer controller regulates the angle of the output voltage of the UPS depending on the demand injected current, while another outer controller sets the reference voltage amplitude to be the equal to the grid voltage. When islanding occurs, the two outer controllers saturate to achieve a seamless mode transition.
In [15], an outer power controller based on the P-w and Q-E droop method is proposed to control the line-interactive UPS in a microgrid. This droop-control-based strategy can regulate the injected power to the grid in the grid-tied mode. More importantly, it can make the UPS systems operate in parallel and share the load automatically without the needs for communication in the islanding mode. This is an essential advantage the aforementioned controllers do not possess. In this sense, the droop-control-based strategy is a prior option to control line-interactive UPSs to form a microgrid. Based on this method, the detailed control strategies for a practical microgrid constructed by two line-interactive UPS systems are presented in [16]. In [15] and [16], the control strategies of line-interactive UPSs are developed based on the assumption that the line impedance is predominantly inductive in a microgrid. This paper presented and discussed a line-interactive UPS system to be used within a low-voltage microgrid where the line impedance is mainly resistive [17]-[19]. The system is based on the Q-w and P-E droop control and can transfer practically seamlessly between the grid-connected and stand-alone modes while sharing the load within a microgrid in parallel with other UPS units. The main novel contributions of this paper are: 1) the analysis, design, and experimental implementation of a new control strategy for line-interactive UPS systems based on the Q-w and P-E droop control, which enables a seamless transfer between the grid-connected and stand-alone parallel modes of microgrid; and 2) a more precise model for designing the controllers is built in the dq-frame based on the instantaneous power definition, which takes into account the dynamic performance of the output impedance of the inverter in the dq-frame and can be evaluated in the time domain.
The paper is organized as follows. The line-interactive UPS and its control strategy are presented in Section II. The limitations of the traditional model to design a controller are discussed in Section III. The new model is deduced and validated by simulation in Section IV. Experimental results from a microgrid consisting of two 40-kW line-interactive UPS systems are given to validate the design in Section V.
II. SYSTEM OVERVIEW AND ITS CONTROL SCHEME
The general overall structure of a low-voltage microgrid, as shown in Fig. 2, consists of DG units, UPS units, local loads, a central controller, and a static transfer switch (STS). The UPS systems are programmed to be voltage sources with the droop control to keep the voltage stable in stand-alone operation and to exchange power with the grid [20]. For example, in the grid-tied mode, the UPS units can be controlled to charge its battery during the grid off-peak tariff and to discharge it during peak tariff periods. When a grid fault occurs, the anti-islanding controllers embedded inside the controllers of the UPS units recognize the fault state and send a signal to the STS and other interfacing units through low-bandwidth communication. Once the signal is received, the STS opens, and the UPS units switch to stand-alone operation and continue to work in parallel to share the power demanded by local loads. After the grid fault is cleared, the PLL module in the central controller starts to work and keeps sending signals of the frequency and voltage to the UPS units. When the reconnecting conditions are satisfied, the central controller sends a signal to close the STS and informs the UPS units to move to the grid-connected operation mode.
Fig. 2.Structure of a low-voltage microgrid.
The microgrid considered in this paper consists of two 40-kW line-interactive UPS systems each powered by a lead-acid battery (320V-450V). The circuit diagram of each UPS system consists of a battery, a dc/dc converter, a bidirectional three-phase dc/ac converter, and a step-up transformer, as shown in Fig. 3. The dc/dc circuit only operates in buck mode, which is composed of Q1, D1 and L1. When active power flows from the grid to the battery, the dc/ac converter operates as a rectifier to control the dc-link voltage (ubat), and the dc/dc converter works to charge the battery. udc is controlled to be higher than the battery voltage (udc). Thus, the diode D2 stays closed. When the power flows in the opposite direction, the buck circuit stops working and the battery supports the dc-link voltage to inject power into the grid through diode D2. Compared to the typical UPS in Fig. 1, the main advantage of this circuit is that the dc/dc circuit can be designed according to the power rating of the battery-charging instead of the discharging capacity. Usually, the latter is much larger than the former in practice. However, its drawback is that the battery voltage needs to be high enough to support the dc-link voltage of the dc/ac converter when power flows from the UPS to the grid. Otherwise, a step-up transformer is necessary, as shown in Fig. 3. The parameters of the main circuit of the UPS are listed in Table I.
Fig. 3.Line-interactive UPS with an unidirectional dc/dc converter.
TABLE IPARAMETERS OF MAIN CIRCUIT
Fig. 4 shows the two-level control of the bidirectional dc/ac converter, called first-level control and second-level control respectively in this paper. The Q-w and P-E droop controllers and an inner voltage controller with a virtual impedance loop construct the first-level control. Variations of the reference voltage () and frequency () are controlled by the second-level control to regulate the power flow in different operation modes.
Fig. 4.Control diagram for the bidirectional dc/ac converter.
In the grid-connected mode, whether the battery is charged or discharged and the demanded power (Pref , Qref) are determined by the command signals from the central controller. During battery-charging (Pref < 0), the dc-link voltage controller operates with the reference voltage udcref set to 600V, and the dc/dc converter charges the battery in either the voltage or current control mode depending on the charging level of the battery. When the discharging command (Pref > 0) is received, the dc-link voltage controller and the dc/dc converter stop operating, and the active power controller starts to work as soon as the dc-link voltage controller quits. To avoid unnecessary transients, any changes of Pref , Qref or udcref should occur gradually via ramp functions.
Upon the occurrence of a power outage, islanding is formed. As soon as the grid fault is detected by the anti-islanding controller, the STS is opened. This means that the microgrid moves to the stand-alone operation mode, and the absolute values of and start to gradually decrease to zero. Finally, all of the UPS systems share the load power properly by the first-level control alone. During the stand-alone mode, and of the parallel UPS units can be uniformly tuned by the central controller to keep the voltage and frequency of the microgrid within permitted levels.
III. LIMITATION OF THE TRADITIONAL MODEL TO DESIGN THE CONTROLLER
Traditionally, the small-signal model of a droop-controlled inverter is deduced through perturbing and linearizing the average power equations [19], [21], [22]. This model is simple and helpful for understanding the essence of droop control. However, in this Section, it is shown to be inadequate for the design of the dc-link controller if the system is designed to have a relatively high bandwidth.
The grid-connected inverter in a microgrid can be modeled by a controllable-voltage source connected in series with an equivalent output impedance, as shown in Fig. 5. Note that all of the variables are the ones converted to the grid side (high voltage side). E and Ug are the voltages of the inverter and the grid, ϕ is the power angle, and Z and θ are the magnitude and phase of the equivalent output impedance of the inverter, respectively. In a low-voltage microgrid, the output impedance is controlled to be mainly resistive (θ ≈ 0), and the output real and reactive powers of the three-phase inverter can be written as follows [19]:
Fig. 5.Equivalent circuit of a grid-connected inverter.
In order to achieve a stable power flow and to improve the dynamics of the system, the following droop functions are used [19]:
where and are the initial reference frequency and voltage fixed by the controller, and are controlled by the second-level controllers to regulate the power flow, and m (n) and md (nd) are the proportional and differential droop coefficients, respectively. Pf and Qf are the measured power signals obtained from filtering P and Q by a low-pass filter FLP(s). Therefore, Pf and Qf can be expressed as:
According to (1) - (3) and considering the integral relationship between the power angel and the frequency, the small-signal models of the frequency droop and voltage droop control loops can be drawn in Fig. 6. Note that the hat symbol ‘ˆ’ refers to the small signal of the quantity, and the over bar ‘¯’ denotes the value at the equilibrium point.
Fig. 6.Small-signal model of the droop controlled inverter.
During battery-charging, the dc-link voltage is controlled by adjusting the amplitude of the output voltage, as shown in Fig. 4, and the is given by:
where kp_dc and ki_dc are the proportional and integral parameters of the PI controller, respectively. The transfer function ûdc(s) / can be expressed as [16]:
where is the battery-charging power, and the linearization point is chosen to be Udc = 600V . According to (4) and (5), the small-signal model of the dc-link voltage control is presented in Fig. 7.
Fig. 7.Small-signal model of the DC-link voltage control.
In order to validate the small-signal models, an actual line-interactive UPS system (seen Fig. 3) is built in PSIM simulation software using the parameters listed in Tables I and II. Note that the detailed parameters of the inner voltage-current controllers are given in Section IV of this paper and no virtual impedance is used. Theoretically, the controller is easy to design to achieve a system with a good stability and a rapid dynamic response. However, the simulation results illustrate that the designed controller, based on the model in Fig. 7, tends to make the system unstable. It also shows that the dynamic response of the small-signal model differs a lot from that of the actual model built in PSIM. For example, when the parameters are selected as kp_dc = 0.08 and ki_dc = 4, Bode plots of the model in Fig. 7 are drawn in Fig. 8, and the step responses of the small-signal and actual models are given in Fig. 9. It can be seen that the Bode plots of the built model in Fig. 8 indicate a stable and well-damped system in contrast with the oscillating one presented by the actual model in Fig. 9.
TABLE IIPARAMETERS FOR THE DESIGN OF CONTROLLERS
Fig. 8.(a) Bode plots of the dc-link voltage control (kp_dc=0.08, ki_dc=4).
Fig. 9.Step responses of the actual model and small-signal mode of dc-link voltage control (kp_dc=0.08, ki_dc=4).
By examining the model in Fig. 7, it can be seen that the transfer function is simply modeled by a constant , which is deduced from the steady-state averaging power function (see (1)) without considering the dynamics of the inverter. This is only reasonable if the control system has a very low bandwidth. Therefore, a more detailed model considering the instantaneous power theory and the dynamics of the inverter is needed.
IV. PROPOSED NEW MODELING METHOD
In this Section, a new small-signal model of a grid-connected inverter with a mainly resistive line impedance is built in the rotating dq-frame. A detailed control diagram of the UPS in the dq-frame is shown in Fig. 10. The frequency of the inverter w is obtained from the frequency droop controller which is used as the rotating frequency of the dq-frame, and ϕi is the angle of the dq-frame. The reference voltage of the inverter is oriented to the d-axis, which means that the q-axis reference voltage is set to be zero, and the real power flow is controlled by adjusting the reference voltage in the d-axis.
Fig. 10.Detailed control diagrams of the grid-connected inverter in dq-frame.
A. Inner Voltage-Current Controllers with a Virtual Impedance
The main circuit of the dc/ac converter is redrawn in Fig. 11. Note that the line impedance and the grid voltage are the ones converted to the inverter side in order to simplify the analysis. The used abc-to-dq-frame transform matrix is:
Fig. 11.Main circuit of the dc/ac converter.
The model for the main circuit shown in Fig. 11 can be described by the following equations [23]:
where are transformed from in the stationary frame. (7) can be depicted in block diagram form, as shown in Fig. 12.
Fig. 12.Model of the main circuit of the grid-connected inverter.
To achieve good dynamics, the positive feedback of the partial output current is used in the inner controllers with α being the feedback coefficient, and to adjust the output impedance of the inverters the virtual impedance loops are also employed, and some additional terms are added to the outputs of the controllers to decouple the control models between the d- and q-axes, as shown in Fig. 13. The used voltage controller Gv(s) , current controller Gc(s) and virtual impedance are expressed as follows:
Fig. 13.Block diagram of the inner controllers of the grid-connected inverter with virtual impedance.
Connecting the models in Fig. 13 and Fig. 12 and discarding the coupling terms, a uniformed model of the inverter with inner double-closed and virtual impedance controllers is represented in Fig. 14.
Fig. 14.Block diagram of the uniformed model of the inverter.
Simplifying the model in Fig. 14, the following equations are obtained:
where:
Gclose(s) and Zodq(s) are the close-loop transfer function and output impedance of the inverter controlled by the inner voltage and current controllers. According to (8), the simplified small-signal model of the inverter can be drawn in Fig. 15.
Fig. 15.Simplified model of the inverter with inner controllers and virtual impedance loop.
B. Power Calculation
The output instantaneous power of the inverter is expressed as:
Disturbing and linearizing (9) around the equilibrium point (Uod , Uoq, Iod, Ioq) yields:
Since the q-axis reference voltage is set to be zero and the output impedance of the inverter is very small, the output voltage of the inverter and the grid voltage at the q-axis are considered to be approximately zero. As a result, the small terms and can be ignored in (10):
C. Power and DC-Link Voltage Controllers
The grid voltage in the stationary frame is assumed to be:
where and ϕg are the amplitude and angel of the grid voltage, respectively. In the dq-frame, the grid voltage can be expressed as:
which is perturbed and linearized around the equilibrium point as follows:
where is the perturbance of the frequency of the inverter obtained from the frequency droop control shown in Fig. 10. It can be seen from (14) that the frequency droop control actually regulates the grid voltage at the q-axis. According to (11), (14), Fig. 10 and Fig. 15, the new-built models of the inverter in the battery-charging and battery-discharging modes can be depicted in Fig. 16. Note that the dc-link voltage controller Gdc(s) is multiplied by the coefficient in order to keep the same meaning as the ones in Fig. 7 (KT is the ratio of the transformer listed in Table I). The used power controllers are:
Gp(s) = kp_p + ki_p/s and Gq(s) = kp_q + ki_q/s.
Fig. 16.Models of the inverter during battery-charging and -discharging operations. (a) Battery-charging mode. (b) Battery-discharging mode.
As shown in Fig. 16, the model has a coupling relationship between the d- and q-axes, and this coupling intensifies as the output reactive power increases. In this paper, the model is tested at the zero-power equilibrium point. As a result, the d-and q-axes models can be evaluated independently.
To compare the new-built models with the conventional ones, the same parameters for the droop controllers and the inner voltage-current controllers are used, as listed in Tables II and III. Fig. 17(a) shows Bode plots of the new-built and conventional models of the dc-link voltage control. It can be seen that the two models have almost the same cross-over frequencies. However, the new model has much less of a phase margin than the traditional one, which means a less damped system than the traditional model does. When the reference voltage udc * is stepped up from 600V to 650V, the simulation responses of the two models and the actual system built in PSIM are shown in Fig. 17(b). As indicated, the response of the actual system is almost the same as the new built model, which is much less damped than the response of the traditional model. Similar results can also be observed when the parameters of the controller are selected as kp_dc=0.2 and ki_dc=2, as shown in Fig. 17(c). To further test the new-built model, an abrupt resistive load change from 0kW to 5kW is applied to the dc side in Fig. 17(d). It can be seen that the dc voltage waveform of the actual system almost coincides with that of the new-built model, which further verifies the accuracy of the new-built model.
TABLE IIIPARAMETERS OF THE INNER CONTROLLERS
Fig. 17.Design of the dc-link voltage controller. (a) Bode plots of the conventional and new-built models of the dc-link voltage control. (b) Step responses of the conventional and new-built models and the actual system. (c) Step responses of the conventional and new-built models and the actual system ( kp_dc=0.2; ki_dc=2). (d) Responses of the new-built model and the actual system at a sudden load increase.
Fig. 18 gives the step responses of the new-built model in Fig. 16(b) and the actual system during battery-discharging. The parameters of the power controllers are listed in Table II. It is found that the waveforms of the power outputted by actual model almost coincide with the ones outputted by the new-built small-signal models. For the sake of clarity, the latter are moved down vertically by 0.1kW and 0.1kVar respectively, as shown in Fig. 18(a) and (b). In addition, it can be seen in Fig. 18 that the reactive power varies little as the output real power increases, and vice versa. This means that there is small coupling between the real and reactive power. This is consistent with the analysis result from the model in Fig. 16 that, at the zero-power equilibrium point, the coupling between the control models of the real and reactive power is very small.
Fig. 18.Power step responses of the new-built model and the actual system. (a) Real power. (b) Reactive power.
V. EXPERIMENTAL RESULTS
An experimental microgrid system with two 40-kW line-interactive UPS units is built to validate the design. The setup is the same with the shadow parts in Fig. 2. The system parameters are the same as those in the simulations, as listed in Table I-III. Six 2-kW 0.25-Ω resistors are used to mimic Fig. 19. The experimental microgrid prototype. the line resistances of the two UPS units. The UPS units and the central controller are implemented digitally using a TMS320F28335 floating-point DSP. The built microgrid prototype is shown in Fig. 19.
Fig. 19.The experimental microgrid prototype.
To test the dynamic performance of the dc-link voltage control system, two experiments are done using one UPS unit in this paper. Firstly, when the UPS works in the battering-charging mode and the demand charging power and reactive power are both set to zero, udcref increases abruptly from 600V to 650V, and the waveforms of the dc-link voltage and phase-B grid-connected current are shown in Fig. 20(a). It can be seen that both the rising time tr and the settling time ts of the dc-link voltage are similar to the simulation results of the small-signal model in Fig. 17(b), where tr is about 0.02s and ts is about 0.1s. Subsequently, the dc-link voltage is controlled back to 600V and a sudden 5-kw resistive load is applied at the dc side of the inverter. The experimental waveforms, as shown in Fig. 20(b), are approximately the same as the simulation ones in Fig. 17(c). As mentioned above, both of the experiments verify the accuracy of the dc-link voltage control model in Fig. 16(b). To validate the capability of the control scheme to realize a seamless transition between the grid-connected and stand-alone modes, more experiments are carried out.
Fig. 20.Dynamic performances of the dc-link voltage control system. (a) udcref stepping up from 600V to 650V. (b) an abrupt load increase from 0kW to 5kw.
Fig. 21 shows the grid-connected-to-stand-alone mode transition of one UPS unit. The UPS unit was operating in the grid-connected mode for charging the battery at a 5-kW rate (note that the current is 180◦ out of phase with respect to the voltage, which means that the UPS is importing power from the grid), and that a 40-kW load is supplied by the grid. When the grid fails, the load naturally transfers to the UPS and does not experience a power interrupt. In addition, the UPS moves seamlessly from the grid-connected mode to the stand-alone mode. It can also be observed that at the moment when the grid fails, the dc-link voltage starts to drop from the active rectifier reference (600 V) to the battery voltage (about 400V) due to a change in the power flow direction.
Fig. 21.Grid-connected-to-stand-alone mode transition of one UPS unit.
Fig. 22 presents the stand-alone-to-grid-connected-mode transition of one UPS unit. The UPS is operating in the stand-alone mode and supplying a 40kW load. When the grid voltage is normal and the mode-transferring order is received, the PLL program module in the center controller starts to work. When the grid-connecting requirements are met, the STS closes, the PLL stops, and the dc-link voltage controller begins to operate. To achieve a smooth load transfer from the UPS to the grid, the dc-link voltage reference starts to increase from the battery voltage at a low rate (0.3V/ms in this paper). As shown in Fig. 22, the output current of the UPS decreases to zero smoothly, and before the current drops to zero, udc increases a little because the UPS is kept outputting real power. After the load transfer is finished, udc increases gradually to the normal reference voltage (600V) and the UPS starts to operate in the grid-connected mode. Note that during the mode transition, the load does not experience a power outage.
Fig. 22.Stand-alone-to-grid-connected-mode transition of one UPS unit.
Fig. 23 shows the mode transition of one UPS unit from battery-charging to battery-discharging. The UPS is charging the battery at a 5-kW rate and the reactive power demand is set to zero. When a 15kW-batter-discharging demand is received, the dc-link voltage controller ceases to work, and the real power controller begins to operate. The real power reference increases at a rate of 50W/ms while udc keeps decreasing. When udc reaches 550V (point A), the battery charger stops working, and udc continues to decrease to the battery voltage (400V). Subsequently, the output power changes its direction and increases gradually to the demand value.
Fig. 23.Battery-charging to battery-discharging transition of one UPS unit.
Fig. 24 gives the waveforms during the grid-connected-to-stand-alone mode transition of the two UPS units. Each unit was charging their batteries at a rate of 5kW. As soon as the grid fails, the two units move seamlessly to the stand-alone parallel mode and share the 40-kW load equally. It can be seen that the load does not experience any power interruptions and the two UPS units behave exactly the same.
Fig. 24.Grid-connected-to-stand-alone mode transition of two UPS units.
Fig. 25 presents the transition of two UPS units from the stand-alone to the grid-connected mode. The two UPS units are operating in parallel in the stand-alone mode, and sharing the 40-kW local load equally. When the transmit order is received and the requirements of reconnecting to the grid are met, the STS closes and the load moves from the UPS units to the grid smoothly, as shown in Fig. 25. The two UPS units behave almost the same as can be seen from their currents waveforms.
Fig. 25.Stand-alone-to-grid-connected mode transition of two UPS units.
VI. CONCLUSION
In this paper, a line-interactive UPS for use in low-voltage microgrids and its control strategy are presented and discussed. The designed system can practically seamlessly transfer from the grid-connected mode to the stand-alone operation mode. The traditional model, based on the average power definition, is verified to be inadequate for use in designing a dc-link voltage controller if the system is designed to have a relative high bandwidth. The new-built model in the dq-frame based on the instantaneous power definition is illustrated to so that it can more precisely describe the dynamics of the system.
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